Notice that .
Can either 1 or 0 be included?
Let be the collection of closed intervals for . What do you notice about ? Is it closed, open, both, or neither?
I'm afraid the wording and available material has got me stumped on this, and being sick at the moment doesn't help.
I should note, the original question said that , but our Prof. told us to change it to when he realized that when and when (or at least that's what I heard him say). I wrote the question word-for-word (besides the change our Prof. gave us), so it doesn't say anything about 0 or 1 being inclusive or not. It just asks us whether the set is open, closed, both or neither.
Point taken. I guess it's a completely open interval, then.
EDIT: One more thing, I've looked at some work done on this in another forum, for which I will provide the link.
http://www.mymathforum.com/viewtopic...=15805&start=0
Is the work found here accurate?